He was a member of the Luftwaffe and a founder of Germany's Green Party. He told tall stories about his life and even taller stories in his art. He gave lectures that lasted 12 hours and once spent a week living in a cage with a wild coyote. His most epic work, entitled 7,000 Oaks, consisted of the planting of exactly that number of trees on his native German soil.

He was Joseph Beuys, fabulist and realist, romantic and activist, a man who made his life into one long, continuous and often seemingly contradictory art performance. Beuys was the last of art's great 20th-century myth-makers, an artist who, since his death in 1986, has attained mythic status. 'He seemed almost a fictional character,' says British artist Cornelia Parker, who, during her student days, travelled to Edinburgh to hear him speak in 1980. 'I was drawn to his work because he was mysterious, a romantic figure with a huge charisma. His attraction was that he was someone I was constantly trying to work out.'

We are still trying to work Joseph Beuys out today, even as his ideas have infiltrated contemporary art to the point where we no longer notice them. His presence is palpable in Hirst's floating shark, in Richard Long's elemental works in stone, in Tracey Emin's tents and quilts, in Jeremy Deller's epic reconstructed dramas, and in Parker's meshing of art with science. This week, Tate Modern hosts Britain's first major retrospective of his work, entitled Joseph Beuys: Actions, Vitrines, Environments . ('Actions' was the term Beuys gave to his performances, many of which tended towards the raw and elemental. Vitrines were the miniature environments he constructed from found objects and materials.) The show is co-curated by the gallery's director, Nicholas Serota, who places Beuys among 'those artists regarded as the most significant of the 20th century'.

After a period where he seemed to have fallen out of favour with the cognoscenti, the Tate show may signal the beginning of a long overdue reappraisal of Beuys's extraordinarily eclectic body of work. Perhaps it is his eclecticism, though, that makes Beuys such a problematic artist. There is an air of unfinished business about most of the work he created, which some interpret as a lack of rigour. On to that work, too, he loaded all manner of often obscure mystical beliefs, insisting, above all, on the now unfashionable notion that art was a magical, even occult, pursuit. Beuys elevated the artist - and himself in particular - to the role of a latterday shaman with the power to heal his own, and the world's, ills.

'I suppose there is what might be called "the quasi factor" about his work - quasi-scientific, quasi-mystical, quasi quite a lot of things,' says Parker, 'but it's not fake. It's just something I personally don't know exactly where to place.'

For all his obscurantism, Beuys also believed passionately in the democratisation of art and the demystifying of the artist. His most famous and oft-stated dictum was: 'Everyone an artist', to which the equally controversial performance artist Gustav Metzger once retorted: 'Every man is an artist; what Himmler too?' Beuys's response went unrecorded.

His work, he said, belonged out in the world, not just in the gallery, but there is a sense still that Beuys, the mythic figure, is somehow bigger than the work. A cult figure while alive, he remains one of those artists whose name is invoked more than his art. 'The exhibitions seem like residues really,' elaborates Parker, 'it's almost like the life was the real art work, the actions spoke louder than the works.'

Even the life, though, was shrouded in mystery and controversy. 'He was a very good Stuka pilot, but not a very good artist,' says Dinos Chapman dismissively, referring to the most controversial example of Beuysian self-mythologising. Though Beuys never tried to hide the fact that he had been a member of the Hitler Youth, he also maintained that he was the pilot of a Stuka that had been shot down over the Crimea during the Second World War. His life had been saved, he said, by a band of Tartars, who covered his burnt body in fat and then wrapped him in felt to keep him warm, hence the recurrence of those same raw materials in his work. German war records subsequently revealed that Beuys had never been a pilot but a radio operator, a trade that does not quite possess the same heroic resonance. The small lie has led some to doubt the veracity of the entire story but this seems not to have perturbed him in the slightest. He was a man who, in life and in art, seldom let the facts interfere with a good story.

Like the Dadaists, Beuys saw absurdism as one response to the horrors of history. In his case, though, it was personal. He was born and raised in Kleve, a small town near Düsseldorf, and, revealingly, was set to pursue an education in medicine when Hitler took power. Whatever the details of his shooting down during the war, he was physically and psychologically altered by his near-death experience and the manner of his survival. His face was badly scarred from the burns he received and he had to have a metal plate inserted in his skull. 'It was a very real and also a very mythologised experience,' elaborates Caroline Tisdall, a close friend of Beuys's who travelled extensively with him, photographing him at work and at play, 'but its impact on his life, and on his work, was immeasurable. It is the single event that made him into an artist.'

After the war, Beuys suffered from severe depression and cured himself by returning to labouring in the fields of his youth. His self-healing continued when he gradually started making small sculptures of animals and objects, all of them imbued with early Christian symbolism or the talismanic symbols of German myths and folklore: the hare, the stag, the oak tree.

'He had a very traditional Catholic upbringing in Kleve, this small Celtic enclave in Germany,' says Tisdall. 'It is called "the Terror Landscape" by Germans because it is so misty and mysterious. He tried always to instil some of that mystery in his work.'

Later, his early grounding in science resurfaced, and his work, bigger and bolder now, began to use what seemed to be conflicting raw materials: electricity and animal fat, batteries and swaths of felt, wire cables and great chunks of stone. Unifying all this was a belief in the primal, transformative power of energy, whether electrical or human, scientific or artistic. In 1961, he took a professorship at Düsseldorf Art Academy, a job that inevitably brought him into conflict with the establishment. He sided with the student activists of the late Sixties and was sacked in 1971 after he led an occupation of the academy's offices. His work, too, had become confrontational, and he was one of the first German artists to explore the nation's uneasiness with its Nazi past.

'In Germany in the Sixties and Seventies, the past was taboo,' says Tisdall. 'The whole Nazi appropriation of the old myths of blood and oak and earth had made even the folk songs taboo. He felt he had to confront the past, and that Germany had to confront it, or it was in danger of becoming what he called "historyless". He said over and over, "A rootless people are a dangerous people."'

His most monumental work, the planting of those oaks in Kassel was a grand ecological gesture, but it also invoked the dark forests of German folklore and, as Tisdall points out: 'It was an artistic reclaiming of the oak tree whose leaves had been used by the Nazis in the decoration of the Iron Cross.' Beuys was also the first German artist to enter a competition for a monument for Auschwitz, and his rejected plan was to create a vast perspective of the railway lines running towards the entrance gates.

In all this, his facing of the buried collective past, and his passionate belief in an ecologically driven future, he was both a prescient artist and a political activist. There was a naivety there, too, though, perhaps best illustrated by his barnstorming attempts to convince the public at large of the healing power of his art. Tisdall remembers him striding though the streets of nationalist Belfast at the height of the Troubles, in felt hat and great coat, engaging local lads, passing pensioners and the occasional tramp in surreal conversations about Celtic mythology.

'He was instinctively drawn to the Celtic fringes, the periphery of Europe, where he believed the old magic was strong. I think that Belfast in 1972 tested that belief somewhat,' she says, laughing.

Nevertheless, Beuys persevered. He walked though 'Free Derry', staged a politically provocative show entitled The Secret Block for a Secret Person in Ireland in Belfast, and lectured to whoever would listen. 'At one point,' Tisdall remembers, 'a bomb went off beside the art college in Bedford Street. There was this huge explosion and a piece of masonry landed at Joseph's feet, a big chunk of concrete with a slice of red brick underneath. He picked it up, turned it over and and said, "Behold! The Northern Irish tongue!" He was pretty unflappable, really.'

His work spoke directly to outsiders such as Jimmy Boyle, now an artist, but back in the early Seventies a prisoner serving a life sentence for murder in the progressive special unit of Barlinnie jail in Glasgow. Boyle was out on day-release when he wandered into an exhibition of Tisdall's photographs of Beuys's action I Like America and America Likes Me, in which the artist had locked himself in a cage with a coyote for a week, protecting himself from its occasional attacks by wrapping himself in felt. Boyle identified directly with the coyote, saying: 'The only worthwhile [art] statement that has had any effect on me and others in my environment has been Joseph Beuys's dialogue with the coyote.' Boyle began a correspondence with Beuys, who later went on hunger strike in protest at Boyle's relocation to another more traditional prison where he was not allowed to make art.

For all Beuys's often wilfully obscure statements and actions, his art, in this instance, communicated its message loudly and clearly, and with a life-changing force. For many of us, though, it remains mysterious, and not always, one suspects, for the reasons that Beuys wanted it to be. That, however, may be the whole point of Joseph Beuys. 'The thinker sees his own actions as experiments and questions, as attempts to find out something,' wrote Nietzsche, the most provocative of all German thinkers. 'Success and failure are for him answers above all.' You suspect that Beuys, even - especially in his sense of mystery and his creation of unfinished art - knew this to be true.

· Joseph Beuys: Actions, Vitrines, Environments is at Tate Modern from Friday until 2 May www.tate.org.uk